Sir John, the former chairman of the Independent Commission on Banking, said he thought the UK “might be a quarter to a third along the path” to implementing the reforms needed to cut the subsidy as he gave evidence to the parliamentary Commission on Standards in Banking.

The precise scale of the implicit state support to the banking system is hard to gauge, but Sir John in his report published last year said some estimates put it “considerably in excess of £10bn”.

Sir John said that the scale of subsidy is being considerably reduced through all the national and international rule changes being put in place since the financial crisis.

He added: “Our view was that much of what we were trying to do was get the UK taxpayer, if not off the hook, then very remote from it.”

Sir John’s report disappointed some by not recommending the full break up of large banks, instead proposing that lenders should put in place a so-called “ring fence” between their retail and investment banking businesses.

Despite the scandals that have emerged since his report was published, such as Libor-rigging and interest rate swap mis-selling, Sir John said he was still against the idea of splitting up banks.

“I am firmly with the recommendation we made. I believe that full separation would have had higher costs for a gain that might not even have been positive,” he said.

“I do not see these events as shifting the balance of the argument against what we proposed, towards total separation.

“I believe the ring-fence will work. With the legal and other safeguards it will work, including on the cultural aspect.”

However, Sir John warned that if banks were found to be “unreformable” it was “possible that total separation would turn out in due course to be the better step to take”.

The parliamentary Commission has already taken evidence from senior policy-makers, including former US Federal Reserve chairman Paul Volcker, who came up with the eponomously named Volcker Rule that prevents US-based banks from certain kinds of risky trading activities.

On Tuesday, chief executives of three of Britain’s largest banks, including Royal Bank of Scotland’s Stephen Hester, Lloyds’ Antonio Horta-Osorio and Standard Chartered’s Peter Sands are due to appear in front of the MPs and Lords to give their views on banking reform.

Submissions to the Commission from the high street banks have already warned of some of the consequences of the reforms, which they have said could impose increased costs on customers for little gain in terms of safety.

The Commission has until December 18 to produce its report and its recommendations are expected to be included in next year’s banking legislation.